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Midterm_Cheat_Sheet Full2.pdf

Mechanical Engineering
Course Code
MECH 3700
Andrew Speirs
Study Guide

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Hollomon’s Equation: 
linear region only
RA: reduction in area
uniform elongation (before onset of necking)
useful up to fracture
true strain as a function of engineering strain
true stress
material properties:
engineering strain at the onset of necking
true stress at the onset of necking
engineering stress at the onset of necking
Fick’s Second Law:
General Solution:
- four basic raw materials in making pig iron &
functions: iron ore; coke fuel; limestone-combines
impurities; hot air-burn coke; use blast furnace
- conversion furnaces: Bessemer-oxygen used to
oxidize carbon and other impurities, oxides form slag
on surface, lime may be added, high N from air can
cause embrittlement; open hearth-air and iron oxides
provide oxygen to oxidize carbon and other
impurities, oxides form slag on surface, limestone
added to control composition of flux to remove
impurities, can produce scrap metal, burns oil, long
cycle, higher quality steel than Bessemer; basic
oxygen (most common)- charged with scrap and
molten iron, oxygen blown into furnace in water-
cooled lance (20 min.), flux (lime) controls slag to
remove impurities, oxygen removes carbon through
intermediate iron oxide product, higher quality than
open hearth; electric arc- oxidation by O2; removes
impurities by slag; electric heat expensive; produces
very high quality steel; Bayer-a mix of ground bauxite
and complex chemical rxns (2NaOH + bauxite →
Na2O∙Al2O3+4H2O+red mud); Hall-Héroult-alumina
converted to Al in electrolytic cells containing cryolite,
Al is deposited on cathode and tapped, cast into ingots
Casting poured at the melting temperature:
Dry interface:
Thickness of fluid layer: 
N: force required to move body along die
F: normal force
: average interface frictional stress
P: normal pressure, often die pressure applied
: material shear strength (temp. dependant)
: effective coefficient of friction
highest effective coefficient of sticking friction is 0.5
: shear strength of absorbed surface film
 average friction of the area of direct and mediated contact
: lubricant velocity
: entrance velocity
: angle of entry
: stress required for forming
`Heat flux is the heat transfer per unit area:
 
S: solidification distance
2.1 Identify two products that you think were made using (a) ingot casting, (b) continuous casting and (c) shape casting. Discuss the reasons for your selections. 2.2
State one advantage and one disadvantage of each of the shape casting techniques described in this chapter. 2.3 Identify the causes of porosity in metal castings.
Explain briefly how each type can be minimized. 2.4 Briefly outline the mechanism responsible for the formation of dendrites in casting a pure metal. Why is dendritic
structure disadvantageous? 2.5 If you sectioned a cast part, you are likely to observe voids within the casting. Explain how you would distinguish between solidification
porosity and gas porosity in terms of the void shape and location. 2.6 The tapered plate shown is to be cast in sand using the horizontal riser/sprue. Explain the
cause of the centreline shrinkage at the location shown. Explain the cause of the centreline shrinkage. Sketch an improved riser/sprue arrangement so that shrinkage in
the tapered plate is avoided. 2.7 (a) Using data from Table 2.3, plot the temperature profile in a large sand mould containing an aluminium casting 5 min after pouring.
(Assume a 1-D conduction heat flow model and a pouring temperature equal to the melting temperature.) (b) Calculate the heat flux flowing from this casting 5 min
after pouring. (c) Calculate the growth rate of the solid-liquid interface 5 min after pouring. (d) Calculate the total thickness solidified after 5 min. 2.8 (a) A very large
iron plate of thickness 100 mm is cast by pouring iron at its melting temperature into a sand mould, such that heat is withdrawn from both faces of the solidifying plate.
Estimate by calculation the time for the plate to solidify if the initial mould temperature is 25 °C. (b) Because in part (a) the iron is cast at its melting point, the liquid
iron sometimes begins to solidify prior to filling the entire mould. To solve this problem the iron is heated to 60 °C above its melting temperature prior to pouring.
Calculate the new solidification time if the initial mould temperature is 25 °C. 2.9 A 10 cm high cylindrical riser is positioned on top of a 10 cm3 cube casting. The riser
extends from the top face of the cube through to the surface of the mould, as illustrated. Assume no heat is lost through the top of the riser to the atmosphere. An
insulator is placed around the riser which effectively doubles the cooling time. Estimate (by calculation) the diameter of the cylindrical riser required to prevent
macroporosity. 2.10 A cylindrical casting is 0.1 m in diameter and 0.5 m in length. Another casting of the same material is elliptical in cross-section, with major axis
twice the length of the minor axis, and has the same cross-sectional area and length as the cylindrical casting. Both pieces are cast using the same conditions. What is the
ratio of the solidification time of the elliptical casting to the solidification time of the circular casting? The perimeter P and area K of an ellipse are:
. 2.11 What are the advantages and disadvantages of using eutectic alloys for shape casting? 2.12 From an Al-Si diagram, you are considering
making a shape casting from two alloys, one containing 2% Si, and the other containing 12% Si. Of these two alloys: (a) which will be more prone to coring, (b) which
will be easier to feed, and (c) which will be more prone to microporosity? 2.13 Why should metals be cooled to a temperature as low as possible prior to casting? 2.14
Calculate the relative amount of H2 absorbed in molten Al cast in an atmosphere where the partial pressure of H2 is  atm, compared to the amount of H2 absorbed in
molten Al in a vacuum where the partial pressure of H2 is  atm. 2.15 The max. eq’m solubility of H2 at a partial pressure of 1 atm in liquid Mg is  per 100 g.
This drops to  per 100 g upon solidification. The density of Mg (liquid and solid) is 
. (a) What would be the gas porosity 
of the Mg casting if liquid
saturated with H2 at 1 atm were allowed to solidify? (b) What partial pressure of H2 should be maintained over the melt if a pore free casting is required? 2.16 How
does the form of carbon in cast iron influence brittleness of cast iron parts? How is the form of carbon in cast iron parts altered to control these properties? 3.1 During
stress-strain tensions tests, many engineering materials exhibit a decrease in engineering stress prior to final fracture. However, the true stress increases continuously
until final fracture occurs. Explain this apparent anomaly. 3.2 A metal has an elongation to failure of 25% and a reduction of area of 50%. Did this metal neck when
tested in uniaxial tension? Support your answer by calculation and explanation. 3.3 During a tensile test of a round metal specimen with an initial diameter of 12.8mm, a
maximum load of 53.4 kN is reached. At this load the cross sectional area is 60% of the starting initial area. Calculate the mean true flow stress of the metal during this
deformation. 3.4 (a) A metal specimen with a cross-sectional area of 5 cm2 is pulled in tension. The UTS is 250 MPa and the cross sectional area corresponding to the
UTS is 4 cm2. Find K and n. (b) If a piece of this metal that is 5 cm wide and 20 m long is deformed, in a drawing manufacturing process, from a thickness of 2 cm to 1.8
cm, what is the ideal work of deformation? (c) Does the calculation of part (b) under- or overestimate the work required for deformation? (d) After the deformation
of part (b), estimate the yield strength of the metal. 3.5 A cylinder of material is compressed at a constant strain rate of  from a starting height of 1 cm to a
height of 0.3 cm. What is the time required for the compression? 3.6 A uniaxial tensile test is performed and the UTS is measured to be 28 ksi. When true stress is
plotted against true strain on logarithmic scales, the experimenter calculates that the strength constant is 50 ksi and the strain hardening exponent is 0.25.
Determine the accuracy of the calculated values. 3.7 True strain can be defined as either  
or 
. With the aid of a typical engineering stress-
engineering strain curve, illustrate the domain for which each of the true strain definitions is not applicable. Give reasons for your answer. 3.8 A fully annealed bar is
deformed from a diameter of 5 mm to a diameter of 4 mm, causing working hardening so that the yield strength of the bar after deformation is 490 MPa. The bar is
then further deformed to a diameter of 3 mm and more work hardening occurs, increasing the yield strength to 603 MPa. The bar is then fully annealed at the 3mm
diameter and the deformed to a diameter of 2 mm. Calculate the yield strength of the bar at the 2 mm diameter. Assume (a) that the strain during deformation does not
exceed the true strain to fracture, and (b) the plastic deformation of the bar obeys the Hollomon equation. 3.9 The initial diameter of a tensile specimen is 10 mm. After
a certain load is applied the diameter is reduced to 8 mm. Calculate the engineering strain and true strain when the diameter is 8 mm. State any assumptions. 3.10 A
metal bar has initial dimensions of 76 mm in length, 12.7 mm width and 7..6 mm thickness. After a load is applied a student measures the new dimensions as 89mm
length, 11.9 mm width and 7.1 mm thickness. Comment on the accuracy of the measurements of the deformed bar. 3.11 A specimen of 10 mm diameter is tensile tested
and a maximum load of 5 kN recorded with a corresponding 20% reduction in the cross-sectional area. A second specimen of the same material is loaded to a true
strain of n/2 (where n is the stress exponent). What load is applied to the second specimen? 3.12 A cylinder is compressed at a constant strain rate of . What is
the time required to compress the cylinder to two-thirds of its original height? What will be the time required to compress the cylinder to one-third of the original
height? 3.13 During a high temperature tensile test of a material, it is noted that changing the strain rate by a factor of 10 increases the true stress by a factor of 3. Is
the material superplastic? Support your answer by calculation. 3.14 A cylinder of 10 cm height and 5 cm2 initial cross-sectional area is hot compressed with a force of 5
kN, the die-workpiece interface is lubricated with boron nitride, which is very effective at reducing friction, and therefore friction effects can be ignored. The hot
deformation equation for the metal of the cylinder is  MPa. Calculate the cylinder height after the force is applied ( 
). 3.15 (a) A metal conforms to
the hot deformation relationship  
 MPa where  
is expressed in . A rod of this material 30 cm long and 1 cm2 cross-sectional area is oriented
vertically, fixed at its upper end and a mass of 10 kg attached to the lower end. Assuming homogenous deformation (and negligible changes in cross-sectional area),
calculate the length of the rod 1 h after loading. (b) From the information provided in part (a), is the deformation behaviour of this material superplastic? State a reason
for your answer. (c) List the four conditions usually necessary for superplastic deformation to occur. 3.16 A 5 cm long, 1.28 cm diameter rod of high strength aluminium
is tested in tension to failure. The yield strength and UTS were found to be 345 MPa and 485 MPa, respectively, and the total elongation to failure is 18%. (a) Calculate
the load at yielding and the load at the ultimate tensile strength. (b) Assuming that necking occurs when the specimen has elongated uniformly by 15%, what is the
instantaneous diameter at the onset of necking? (c) What is the true stress at the onset of necking? (d) What are the values of n and K for the Hollomon equation? 4.1
Identify two advantages of hot working versus the cold working of metals. 4.2 A cylinder () is compressed by an open die forging process. The
true strain to fracture the cylinder is  and the governing deformation relationship is  MPa. The lubricant provides a friction coefficient of 0.1. The
process is limited by either platen yielding or fracture. If the yielding stress of the platens is 800 MPa, do the platens yield of does the specimen fracture?
Heat transfer during continuous casting:
Estimate solidification time:
Sand casting sprue:
Gas porosity (Sievert’s Law):
macroporosity-liquid shrinkage, solidification
shrinkage, solid shrinkage, low fluidity;
microporosity-decreased strength and fatigue life,
trapped within dendrite growth, trapped liquid
solidifies and shrinks, shrinkage volume must be filled
by more liquid (requires low viscosity to flow through
dendritic structures, viscosity of liquid near melting
temperature, and thus in mushy zones, tends to be
very high, micropores form as a result, change alloy to
reduce mushy zone, increased temperature gradients
also reduce size of mushy zone and promote
nucleation, avoid long, thin sections, faster liquid
shears dendrites; gas porosity-gases more soluble in
liquid than in solid (mostly H2), sudden decrease in H2
solubility from solidification causes formation of H2
bubbles in interior, spherical
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